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A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...

The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

A type of maximal Abelian subgroup.

The relationship Sq^i(x cup y)=Sigma_(j+k=i)Sq^j(x) cup Sq^k(y) encountered in the definition of the steenrod algebra.

The antisymmetric parts of the Christoffel symbol of the second kind Gamma^lambda_(munu).

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

The matrix decomposition of a square matrix A into so-called eigenvalues and eigenvectors is an extremely important one. This decomposition generally goes under the name ...